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Feb
2
comment Does this notion related to species/operads/FI-modules have a name?
Perfect! Thanks.
Feb
2
accepted Does this notion related to species/operads/FI-modules have a name?
Feb
2
asked Does this notion related to species/operads/FI-modules have a name?
Jan
31
answered $\mathbb{A}^1$-invariance of categories of Finite Etale Covers
Jan
31
comment Reference request for a “truncated version” of the de Rham algebra
In Hodge theory one often considers the "dual" truncation to the one you describe (although on the holomorphic de Rham complex), setting all forms below a certain degree to zero. This is what gives rise to the Frölicher spectral sequence, and the Hodge filtration on the cohomology of a compact Kähler manifold.
Jan
30
comment $\mathbb{A}^1$-invariance of categories of Finite Etale Covers
What's the characteristic of $k $?
Jan
22
awarded  Good Question
Jan
20
awarded  Nice Answer
Jan
19
answered When can the “homotopy exact sequence” of etale fundamental groups for a smooth curve fail to be exact?
Jan
13
answered factorization of the cohomology of configuration space
Dec
10
comment Does the Grothendieck ring of varieties contain torsion?
Hm. This is not completely convincing, is it? You're saying "If the Grothendieck ring contained torsion then this would resolve problems known to be hard, so the problem is surely open". But it's also possible that the Grothendieck ring does not contain torsion; this could very well be easier to show than Hausdorffness of the $\mathbb L$-adic topology, right?
Nov
30
comment A lift of the second Chern class
@PavelSafronov Thanks. To be perfectly honest, I have no clue whether there is a higher algebraic gerbe lying around...
Nov
29
comment A lift of the second Chern class
@PavelSafronov Your last sentence is a bit weird - why do you say that the Chern classes in Chow are "totally different" for $n \geq 2$? The cycle map from Chow ring to Deligne cohomology is compatible with the Chern classes for all $n$. Do you just mean that the map $\mathrm{CH}^n(X) \to H^{2n}_{\mathcal D}(X,\mathbf Z(n))$ is not an isomorphism in general for $n \geq 2$?
Nov
25
comment Does the nearby cycle functor commute with the Verdier duality?
I mean the version which includes a degree shift of -1 compared to the "naive" definition of nearby and vanishing cycles. With this degree shift the functors send perverse sheaves to perverse sheaves and commute with Verdier duality. Otherwise they just commute with Verdier duality up to a degree shift.
Nov
25
answered Does the nearby cycle functor commute with the Verdier duality?
Nov
18
awarded  Nice Answer
Nov
16
comment About the decomposition of a Chow group of a variety
I guess I should've said "Chow ring" rather than "Chow group" - I meant splitting compatibly with the intersection product.
Nov
14
answered About the decomposition of a Chow group of a variety
Nov
6
awarded  Popular Question
Nov
4
comment What happens to the gonality under a finite morphism of curves
@FelipeVoloch I didn't assume the cover is unramified either. The covering map gives an extra involution of $C$, which must come from an involution of $\mathbf P^1$ permuting the branch points of the hyperelliptic map. It follows that $C$ has affine equation $y^2=f(x^2)$ and $C'$ has equation $y^2=f(x)$ or $y^2=xf(x)$.